Answer by François G. Dorais for Definable collections without definable...
There is a nice model-theoretic interpretation of the property you state, which I will call property (A). By a theory of sets, I mean any theory $T$ with an extensional relation ${\in}$.Fact 1. If $T$...
View ArticleAnswer by Joel David Hamkins for Definable collections without definable...
Update. (June, 2017) François Dorais and I have completed a paper that ultimately grew out of this questions and several follow-up questions. F. G. Dorais and J. D. Hamkins, When does every definable...
View ArticleDefinable collections without definable members (in ZF)
Denote Zermelo Fraenkel set theory without choice by ZF. Is the following true: In ZF, every definable non empty class A has a definable member; i.e. for every class $A = \lbrace x : \phi(x)\rbrace$...
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